Two-Level Theories and Fuzzy Sets Gary Goertz Department of Political Science University of Arizona Tucson, AZ 85721 email: [email protected] and James Mahoney Department of Sociology Brown University email: James [email protected] 21 January 2004 An earlier version of this paper was presented at the Second Annual Training Institute on Qualitative Re- search Methods, Arizona State University. For helpful comments and advice, we thank Charles C. Ragin. James Mahoney’s work on this material is supported by the National Science Foundation under Grant No. 0093754. This paper can be downloaded from ftp://128.196.23.212/iqrm/goertz mahoney2004.pdf A “teaching” version of this paper is available from the authors. It is a lightly-edited version of the current paper with exercises and answer key.
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Two-Level Theories and Fuzzy Sets
Gary GoertzDepartment of Political Science
University of ArizonaTucson, AZ 85721
email: [email protected]
and
James MahoneyDepartment of Sociology
Brown Universityemail: [email protected]
21 January 2004
An earlier version of this paper was presented at the Second Annual Training Institute on Qualitative Re-search Methods, Arizona State University. For helpful comments and advice, we thank Charles C. Ragin.James Mahoney’s work on this material is supported by the National Science Foundation under Grant No.0093754. This paper can be downloaded from ftp://128.196.23.212/iqrm/goertzmahoney2004.pdf
A “teaching” version of this paper is available from the authors. It is a lightly-edited version of the currentpaper with exercises and answer key.
Gary Goertz teaches political science at the University of Arizona. His books includeInter-national Norms and Decision Making: A Punctuated Equilibrium Model(Rowman & Littlefield,2003),Contexts of International Politics(Cambridge University Press, 1994), and with Paul F.Diehl Territorial Change and International Conflict(Routledge, 1992) andWar and Peace in In-ternational Rivalry(University of Michigan Press, 2000). He is coeditor with Harvey Starr ofNecessary Conditions: Theory, Methodology, and Applications(Rowman & Littlefield, 2002).
James Mahoney is an associate professor of sociology at Brown University. He is the authorof The Legacies of Liberalism: Path Dependence and Political Regimes in Central America(JohnsHopkins University Press, 2001), which received the Barrington Moore Jr. Prize of the Compar-ative and Historical Sociology Section of the American Sociological Association. With DietrichRueschemeyer, Mahoney is coeditor ofComparative Historical Analysis in the Social Sciences(Cambridge University Press, 2003). He has published articles on causal analysis in small-N re-search, path dependence in historical sociology, and long-run development and political change inLatin America.
Abstract
Two-level theories explain outcomes with causal variables at two levels of analysis that are sys-tematically related to one another. Although many prominent scholars in the field of comparativeanalysis have developed two-level theories, the empirical and methodological issues that these the-ories raise have yet to be investigated. In this article, we explore different structures of two-leveltheories and consider the issues involved in testing these theories with fuzzy-set methods. Weshow that grasping the overall structure of two-level theories requires both specifying the partic-ular type of relationship (i.e., causal, ontological, or substitutable) that exists between and withinlevels of analysis and specifying the logical linkages between levels in terms of necessary andsufficient conditions. We argue that for the purposes of testing these theories fuzzy-set analysisprovides a powerful set of tools. However, to realize this potential, investigators using fuzzy-setmethods must be clear about the two-level structure of their theories from the onset. We illustratethese points through an empirical, fuzzy-set test of Skocpol’sStates and Social Revolutions.
With rare exceptions, theories utilize nonhierarchical, single-level causal structures. Whether sta-tistical or qualitative, the results of the empirical analysis are represented in one equation. In thisarticle, we show thattwo-leveltheories have distinctive theoretical properties and advantages, andin fact that many prominent theories really are two level in nature.
Two-level theories offer explanations of outcomes by conceptualizing causal variables attwo levels of analysis that are systematically related to one another. One level represents the coreof the theory, focusing on the central causal variables and main outcome under investigation. Thevariables at this level refer to easily grasped and remembered concepts around which our socialscience vocabulary is primarily organized. We use the expression “basic level” to describe this partof the theory (c.f., Brown 1965; Rosch et al. 1976). A second level focuses on causal variables ata less central level of aggregation, often at a lower level. The variables at this “secondary level”are also causes of the main outcome under investigation, but their effects cannot be understoodindependently of their relationship with the causal factors at the basic level. Thus, one must graspthe structure of the relationship between the basic level and the secondary level before the theoryas a whole can be understood and evaluated.
We explore different structures of two-level theories and examine the methodological issuesinvolved in employing fuzzy-set analysis test to these theories. We are centrally concerned withtheories that propose relationships among variables using ideas about necessary and sufficient con-ditions. At either level, we examine two specific logical structures: (1) a set of causal factors thatare individually necessary and jointly sufficient; and (2) a set of causal factors that are individuallysufficient but not necessary. These kinds of causal relationships are commonly formulated in com-parative studies, and they can be usefully analyzed with Ragin’s (1987; 2000) methods. However,methodologists have yet to explore either of these causal structures in the context of two-leveltheories.
We also focus attention on how variables at a secondary level relate to the causal variablesof the basic level. We examine three possible theoretical relationships: causal, ontological, andsubstitutable. With a causal relationship, the variables at the secondary level are treated as thecauses of the causal variables at the basic level. In this sense, one can think about this kind ofrelationship as modeling “causes of causes.” With an ontological relationship, the variables atthe secondary level represent features that define or constitute causal variables at the basic level.These secondary-level variables arenot indicators of the basic-level variables, but rather are theelements that literally constitute basic-level phenomena. Finally, with a substitutable relationship,the variables at the secondary level are different ways by which it is possible arrive at basic-level states. Here secondary-level variables often refer to alternative means of achieving endsrepresented by variables at the basic level.
Ideas of necessary and sufficient conditions are essential to understanding each of thesethree relationships. For example, an ontological relationship traditionally has referred to a set ofsecondary-level variables that are necessary and sufficient for the existence of a given basic-levelvariable; in the classical approach to concepts, categories are defined via necessary and sufficientconditions (Sartori 1970; Collier and Mahon 1993; Lakoff 1987). A substitutable relationshiprefers to a set of secondary-level variables that are individually sufficient but not necessary for thepresence of a given basic-level variable; they are various means to attain a given end (Most andStarr 1984). Finally, a causal relationship might be characterized by either necessity or sufficiency,including complex combinations of the two. Grasping the link between the secondary level and thebasic level therefore requires both specifying the theoretical nature of the relationship (i.e., casual,ontological, or substitutable) and specifying the logical structure of the relationship in terms ofnecessary and sufficient conditions.
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While we shall see that several well-known theories have a two-level structure, two-leveltheories have not been recognized as such in the literature. Cioffi-Revilla (1998; see also Cioffi-Revilla and Starr 2002) provides perhaps the only exception. He describes and analyzes two-levelstructures that clearly are hierarchical and that relate variables across levels using necessary andsufficient conditions. This work nicely compliments the present analysis. Cioffi-Revilla presentstwo-level theories in an abstract and mathematical manner, while we stress the many applicationsin the area of qualitative comparative research. In addition, Cioffi-Revilla is thoroughly proba-bilistic in his approach. He thus shows that one cannot object to necessary and sufficient conditionstructures as being inherently deterministic.
Our discussion proceeds in two parts. In part one, we focus on the structure of two-leveltheories. We consider the common features found across all two-level theories as well as thedistinctive types of these theories. In terms of distinct types, we examine both alternative logicalstructures that can characterize causal relations at the basic level and alternative relationships thatcan exist between the secondary level and the basic level. We then concretely illustrate thesealternative possibilities with substantive examples from leading works in the field of comparativeanalysis.
In part two, we turn our attention to the use of fuzzy-set analysis as a tool for testing two-level theories. We focus here on Skocpol’sStates and Social Revolutions(1979) as an extendedexample because it is a famous study that has been at the center of much methodological debate.We suggest that our analysis provides for the first time a succinct and accurate portrayal of thestructureof Skocpol’s theory. In addition, we provide the first test of this theory using fuzzy-settechniques.
We conclude that fuzzy-set methods are very helpful for testing two-level theories becausethey allow the analyst to think about complex causal patterns in terms of necessary and sufficientconditions. Yet these methods will have problems evaluating two-level theories if one is not clearabout the structure of these theories from the onset. For example, a fuzzy-set test that focuseson variables of the secondary level will not generate meaningful results unless the relationshipbetween these variables and basic-level causes is systematically considered. Hence, analysts mustconsider the overall structure of a two-level theorybeforeevaluating it using fuzzy-set techniques(or any other method).
Based on our discussion, we offer a number of suggestions for scholars who seek to de-velop two-level theories and test them using fuzzy-set methods in the future. We call for greaterexplicitness about the nature of the relationship between secondary and basic-level variables. Wealso urge investigators to think through and carefully justify the logical procedure through whichsecondary-level variables are used to generate basic-level variables. Different procedures producedifferent variable scores at the basic level, with large implications for the evaluation of the overalltheory.
The Structure of Two-Level Theories
In this section, we describe the common structure of two-level theories, drawing on the conceptsof basic level and secondary level. We also examine different logical structures that can exist atthe two levels, and the different kinds of relationships that can exist between the secondary leveland the basic level.
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Basic Level
In a two-level theory, the basic level contains the main causal variables and outcome variable ofthe theory as a whole. A typical summary of a two-level theory will focus on the concepts andargument contained within the basic level. We adopt the label “basic level” from the work ofBrown (1965), Rosch and her colleagues (Rosch et al. 1976), and other cognitive scientists whostudy categorization (see Lakoff 1987, esp. chap. 2). These analysts have found that ordinarylanguage users prefer to communicate and think at a certain level of aggregation, which they callthe basic level. For example, we learn and use basic-level concepts like table and chair morereadily than more general concepts like furniture or more specific ones like stool. We believe thatthe same practice applies to the social sciences. Social scientists name and remember things moreeasily at a certain level of analysis and thus organize much of their thinking and arguments at thisbasic level. For example, contemporary social scientists are more likely to build their main theoriesaround concepts such as democracy, war, and welfare state as opposed to concepts at higher levelsof analysis (e.g., political system, violence, and public policy) or lower levels of analysis (e.g.,federal democracy, internal war, or maternal welfare state).1
Variables at the basic-level form the building blocks of two-level theories, but there are dif-ferent logical structures through which these variables can be put together. We find that muchqualitative and comparative work uses two logical structures at the basic level: (1) a set of causalfactors that are individually necessary and jointly sufficient for an outcome; and (2) a set of causalfactors that are individually sufficient but not necessary for an outcome. We refer to the first struc-ture as a “conjuncture of necessary causes” to highlight the fact that a combination of necessaryconditions are sufficient to produce an outcome. We refer to the second structure using the term“equifinality,” which means that there are various conditions that are sufficient to produce the sameoutcome and hencemultiple pathsto the same outcome (see Ragin 1987). For example, a classicexample of equifinality is Barrington Moore’s (1966) argument that there are three independentroutes to the modern world.
The underlying logical structure of a conjuncture of necessary causes can be specified sim-ply as:
Y = X ∗ Z (1)
In this equation, we have two necessary conditions (X andZ) that are jointly sufficient forY. Weuse the asterisk to signify the logical AND. Because the equation indicates that a case must be amember ofX andZ to be a member ofZ, we can refer to this basic structure as characterized byAND.
The second logical structure is equifinality. In contrast to equation (1), there are no neces-sary conditions in this structure. Instead, there are multiple paths by which Y can occur:
Y = X + Z (2)
Equation (2) provides this structure in that the plus sign designates the logical OR, such thatX orZ is sufficient forY. Hence, equifinality is a logical structure characterized by OR.
These two types are not the only options for representing causal structures at the basic level.For example, one could have a basic level theory that simply focused on individually necessarycauses. Likewise, one could easily formulate more complex hybrid structures such as:
Y = U ∗ X + U ∗ Z (3)
1Yet, it would be wrong to see the basic level as single fixed point shared by all scholars. The exact level of cate-gorization that corresponds to the basic level may vary across scholarly circles depending on expertise and knowledge,much as is true with the basic level of ordinary concepts for different cultural communities.
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In equation (3), we have both a necessary condition (i.e.,U) and equifinality (i.e.,U andX or UandZ). For the purposes of this paper, we will focus our discussion of the basic level on the twocanonical causal structures of equifinality and a conjuncture of necessary causes.
Secondary Level
Variables at the secondary level are less central to the core argument and refer to concepts that areless easily remembered and processed. Nevertheless, these variables play a key theoretical role.For example, in theories about democracy, the variables of free elections, civil liberties, and broadsuffrage often play a major role, even though they are still secondary compared to the basic-levelconcept of democracy itself.
Three relationships can exist between the secondary level and the basic level: causal, on-tological, and substitutability. It bears emphasis that none of these relationships is simply one inwhich the secondary-level variables serve as indicators or measures of the basic-level variables.The role of the secondary-level variables isnot to operationalize the basic-level variables. Rather,in a two-level theory, the secondary-level variablesalways have a causal relationship to the mainoutcome variable. Two-level theories are complex precisely because the nature through whichsecondary-level variables affect the main outcome variable varies depending on how these vari-ables relate to the causal variables at the basic level.
First, there may be acausal relationshipbetween secondary-level variables and basic-levelcausal variables; in this case, secondary-level variables represent “causes of causes.” With a causalrelationship between levels, the secondary-level variables affect the main outcome variable byhelping to bring into being more temporally proximate causal variables at the basic level. Hence,when a causal relationship exists between levels, one can usefully speak about more remote causes(i.e., secondary-level causes) and more proximate causes (i.e., basic-level causes).
The logical structure of the causal relationship between variables at the two levels can vary.For example, either the conjuncture of necessary cause structure or the equifinality structure dis-cussed above in equations (1) and (2) could apply. Alternatively, the secondary-level variablescould be individually necessary but not jointly sufficient for the basic-level variables or somemore complex formulation. Below we consider different alternatives.
Second, anontological relationshipcan exist between levels. In this case, the secondary-level variables represent the defining features that constitute the basic-level variables; the secondary-level variables literallyare the elements that compose the basic-level variables. For example, freeelections, civil liberties, and broad suffrage might be treated as the ontological secondary-levelvariables that constitute the basic-level variable of democracy. We use the word “ontological” todescribe this relationship because it stresses that the issue concerns the essential character, struc-ture, and underlying parts of the phenomenon to which the basic-level concept refers. In addition,ontological is preferable to alternatives such as “descriptive” or “definitional” because, in a two-level theory, the secondary-level variables play a key causal role in explaining why the basic-levelcausal variables have the effects they do. For example, the institutional theory of the “democraticpeace” invokes elections as a key part of the explanation for why democracies do not fight warswith each other. In this theory, the ontological secondary-level variable of elections (which in partdefines the basic-level concept of democracy) has a causal impact on the main outcome variableof war.
The logical structure of an ontological relationship can take different forms. Traditionally,most scholars have defined concepts in terms of necessary and sufficient conditions. For example,the classical approach to concepts built around a taxonomical hierarchy, as exemplified by Sartori
4
(1970), treats defining attributes (secondary-level variables) as necessary and sufficient for mem-bership in a concept (a basic-level variable). With the classical approach, the analyst uses AND toconnect the secondary-level variables with the basic-level variable.
Although the classical approach is frequently employed, the work of Collier and his col-laborators (Collier and Mahon 1993; Collier and Levitsky 1997) shows that alternatives do exist.Most notably, the family resemblance idea (Wittgenstein 1968) embodies the logical structure ofequifinality rather than necessity. By definition, family resemblance means that there are no nec-essary conditions (i.e., no single trait is shared by all members of the family). Instead, as long ascases have enough characteristics associated with the family, these cases are members of the fam-ily. Hence, the family resemblance structure is one of sufficiency without necessity, the hallmarkof equifinality.
To connect the secondary-level variables with the basic-level variable in the family resem-blance structure, the analyst uses OR. However, because the family resemblance structure mayrequire that more than one secondary-level variable must be present for membership in the ba-sic level, the strict application of OR will not always be adequate (i.e., the presence of a singlesecondary-level variable maynot be sufficient for membership in the basic-level category). In-stead, the structure can be better modeled by another version of OR that implements the rule that“m of n characteristics must be present.” Thus, when considering the ontological family resem-blance structure, we propose to implement OR as follows:
Y = min(sum(X1, X2, . . .), 1) (4)
Equation (4) is a fuzzy-set logic implementation of the family resemblance m-of-n rule.2 Whenusing this implementation, the values of the secondary-level variables are calibrated to reflectthe number of attributes that must be present for a case to be a member of the basic level. Forexample, if at least two of four possible attributes must be present to be a member, then the valuesof the secondary level variables should be set to a maximum of .50 (e.g., if the variable is codeddichotomously, its possible values would be 0.00 and .50). Hence, if two secondary level variablesare present, the case would be a member of the family (i.e., the sum of .50 and .50 is 1.00). If onlyone secondary-level variable is present, the case would be excluded from full membership. Weuse the expression min(sumXi,1) to characterize this procedure for implementing OR.
Finally, we consider asubstitutable relationshipbetween the secondary and basic levels. Inthis case, the secondary-level variables are neither causes nor constitutive features of the basic-level causal variables. Rather, each secondary-level variable is a substitutable means to a givenbasic-level variable. At the basic level is a concept such as “labor incorporation” (Collier andCollier 1991). Substitutability at the secondary level is an analysis of the different ways that laborcan or has been incorporated in different countries. In some countries this incorporation occurredvia political parties, while in others it has been done by the state. Cioffi-Revilla (1998) stresses thatsubstitutability is related to redundancy in systems (e.g., Bendor 1985; Landau 1969). Systemsare more stable if necessary components have backups and alternative sources. An example is theUS nuclear deterrence via the triad of air, land, and submarine-based weapons. If any one or twolegs of the system were to be taken out by attack, there is enough redundancy in the system to givethe United States a second strike capability (Cioffi-Revilla 1998).
Two-level theories are thus distinctive and powerful precisely because secondary-level vari-ables are systematically related to basic-level variables. The addition of the secondary-level vari-ables not only adds complexity to the argument developed at the basic level, but also helps analystsempirically substantiate the argument at the basic level. To concretely test the claims at the basiclevel, analysts must draw on the information at the secondary level, which allows them to move
2In fuzzy-set logic there are various ways to implement OR; see Smithson 1987 for a discussion.
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down (or occasionally up) levels of analysis and examine data that further elaborates the causal re-lationship. For example, the examination of an ontological relationship between levels allows theanalyst to explore the specific defining properties of the basic-level concepts that actually affectthe outcome of interest. In this case of an ontological relationship, the specific properties identifiedin the secondary level are “mechanisms” that explain why the basic-level variables have the effectsthey do. Substitutability is usually pursued when the analyst needs to explore the different ways inwhich the basic-level process can be fulfilled. Here the basic level taps a factor which is commonacross cases (e.g., labor incorporation), while the secondary level permits differentiation amongcases in the ways in which this can occur (e.g., state or party incorporation of labor). Finally, acausal relationship enables the researcher to deepen the analysis by adding an account of the moretemporally removed processes that bring into being the proximate basic-level causes themselves.This approach is highly effective when the basic-level causes are very closely related to the mainoutcome of interest.
In this discussion, we have emphasized different ways in which secondary-level variablescan relate tocausalvariables at the basic level. However, two-level theories that propose an on-tological relationship may consider the linkage between secondary-level variables and the mainoutcomevariable at the basic level. In doing so, the theory draws on the secondary level to ex-plicate and conceptualize the basic-level outcome variable. When analysts define their outcomevariable in terms of secondary-level variables, they are offering an ontological and conceptualaccount of how secondary-level variables relate to the basic-level outcome variable.
In sum, the various relationships that may characterize two-level theories are complex.Given this complexity, it is helpful to elaborate the structure and propositions of two-level the-ories in visual format. Below we shall do this by presenting several figures that diagram thestructure of different two-level theories. Because two-level theories have not been systematicallyconsidered in the literature, we offer a new system of symbols to represent different possible re-lationships. In the discussion below, we use the following symbols for representing the elementsand relationships of two-level theories:
• We shall use bold face characters for the basic-level variables and regular roman type forthe secondary-level variables.
• We shall represent a causal relationship with a solid arrow pointing from the cause to theoutcome:...................................................................... ..............
• We shall represent an ontological relationship with a sequence of equal signs:
• We shall represent a substitutable relationship with a dotted arrow:............................ ......
• We shall designate the logical AND with the asterisk symbol: *
• We shall designate the logical OR with the plus sign: +
• We shall represent a conjunction of necessary conditions that are jointly sufficient as fol-lows: ...................................................................... .............. ....................................................................................
Table 1 summarizes the three theoretical relationships between levels (causal, substitutabil-ity, and ontological) along with the two alternative structures that can be used at either level (con-juncture of necessary conditions or equifinality). Clearly, we have a variety of theoretical andlogical possibilities. Thus two-level theories form aclassof theories. Because there are two lev-els, two logical structures, and three relationships between levels, we have a powerful set of toolsto model social phenomena. In an important sense, two-level theories are one implementation of
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Table 1: Relationships From the Secondary Level to the Basic Level
RelationshipDependent Necessary
Equifinality FigureTemporal
variable condition Priority
Causal No Yes Yes ...................................................................... .............. YesSubstitutability No No Yes ............................ ...... NoOntological Yes Yes Yes No
George and Bennett’s (forthcoming) notion of typological theory. Combining the possibilities intable 1 generates a rich typology of theoretical structures.
Not only do two-level theories provide a framework for future theorizing, we suggest thatthey are very useful in understanding existing theories. Many social theorists have implicitlythought in two-level terms. Much of the confusion around some theories, e.g., Skocpol (1979),arises from a failure to appropriately conceptualize levels and relationships between levels. In thenext section, we provide some examples of what two-level theories look like in practice.
Substantive Examples of Two-Level Theories
In this section, we offer several different examples of two-level theories. Since the concept of atwo-level theory is not prominent in the literature (though see Cioffi-Revilla 1998; Cioffi-Revillaand Starr 2002), we must interpret the degree to which the studies in question are two-level theo-ries. In addition, we must uncover the specific two-level theoretical structures of the studies, sincethey are not explicitly developed. We have tried to focus on clear examples of two-level theoriesthat exhibit some of the different possible theoretical structures. At the same time, we wish to beclear that what follows are ourstylized reconstructionsof authors’ works – reconstructions thatinevitably simplify more sophisticated arguments.
Skocpol’s Theory of Social Revolution
We begin with Skocpol’sStates and Social Revolutions(1979), which seeks to explain the onsetof social revolution in France, Russia, and China through a comparison with several other casesthat did not experience social revolution. Despite all the attention surrounding this work, mostanalysts have failed to recognize its two-level structure. In figure 1, we summarize that structure.
Basic Level. At the basic level,States and Social Revolutionshas the structure of a conjunctureof two necessary causes that are jointly sufficient for the outcome of social revolution. Skocpolsummarizes these two basic-level causes as follows:
“I have argued that (1) state organizations susceptible to administrative and militarycollapse when subjected to intensified pressures from more developed countries fromabroad, and (2) agrarian sociopolitical structures that facilitated widespread peas-ant revolts against landlords were, taken together, the sufficient distinctive causesof social-revolutionary situations commencing in France, 1789, Russia, 1917, andChina, 1911” (1979, p. 154).
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These two causes refer to conditions for state breakdown and conditions for peasant revolt, andthey can be summarized simply as “state breakdown” and “peasant revolt.” Because these variablesare at the basic level, most (good) summaries of Skocpol’s work have referred to them.
Skocpol is explicit that these two causes are jointly – not individually – sufficient for socialrevolutions. This is clear from her assertion that the two factors “were, taken together, the sufficientdistinctive causes . . . ” and from her explicit remarks that state breakdowns would not have led tosocial revolutions without peasant revolts (1979, p. 112). Elsewhere she attempts to empiricallydemonstrate that neither condition is by itself enough to produce social revolutions by contrastingcases of non-social revolution in which only one of the two conditions was present.
It is harder to find explicit passages inStates and Social Revolutionswhere Skocpol statesthat her key variables arenecessaryfor social revolution. But there are passages that strongly hintat the necessary condition character of her two core variables. For example:
Nevertheless, peasant revolts have been the crucial insurrectionary ingredient in vir-tually all actual (i.e., successful) social revolutions to date . . . Without peasant revoltsurban radicalism in predominantly agrarian countries has not in the end been able toaccomplish social-revolutionary transformations . . . they [English and German revo-lutions of 1848] failed as social revolutions in part for want of peasant insurrectionsagainst landed upper classes” (1979, p. 113).
In addition, Skocpol has been widely interpreted as identifying necessary causes (e.g., Kiser andLevi 1996, 189–90; Dion 1998) and her work is used by Ragin (2000) as central example of nec-essary conditions: “Consider the argument that both ‘state breakdown’ and ‘popular insurrection’are necessary conditions for ‘social revolution’ ” (p. 219).
The basic-level argument ofStates and Social Revolutionstherefore has the formal structureof equation (1), which we call a conjuncture of necessary causes. Here we succinctly – and perhapsfor the first time in print – state Skocpol’s basic theory of social revolutions:
State breakdown and peasant revolt are individually necessary and jointly sufficientfor social revolution.
This proposition is bound by certain scope conditions, such as the presence of an agrarian-bureaucraticstate that lacks a significant colonial history. Within the scope identified by Skocpol, however,state breakdown and peasant revolt represent a combination of individually necessary and jointlysufficient variables.
Secondary Level. At the secondary level, Skocpol focuses on the different processes that canproduce state breakdown and peasant revolt. In this sense, there is acausal relationshipbetweensecondary-level variables and basic-level causes. The logical structure of this causal relationshipis one of equifinality – that is, the secondary-level variables are individually sufficient but not nec-essary for either state breakdown or peasant revolt. Formally, to characterize Skocpol’s argumentin this way, we use OR at the secondary level of the theory. Hence, whereas Skocpol’s theory isbuilt around a causal conjuncture of necessary conditions at the basic level, it is characterized byequifinality at the secondary level.
With respect to explaining the basic-level cause of state breakdown, Skocpol focuses heranalysis on three secondary-level causes: (1)international pressure, which promotes crises forregime actors; (2)dominant-class leveragewithin the state, which prevents government leadersfrom implementing modernizing reforms; and (3)agrarian backwardness, which hinders nationalresponses to political crises. With respect to peasant revolt, Skocpol focuses on two secondary-level variables: (1)peasant autonomy and solidarity, which facilitate spontaneous collective action
9
by peasants; and (2)landlord vulnerability, which allows for class transformation in the country-side.
Skocpol’s theory not only relates secondary-level variables to the causal variables of thebasic level, but it also directly relates secondary-level variables to the outcome variable of socialrevolution itself. Here, however, the relationship is ontological; we have a theoretical structure ofwhat social revolutionis – i.e., the defining features of the concept.
In classical fashion, Skocpol defines social revolution using a necessary and sufficient con-dition structure: “Social revolutions are rapid, basic transformations of a society’s state and classstructures; and they are accompanied and in part carried through by class-based revolts from be-low.” (1979, pp. 4–5). This definition holds that social revolutions are the combination of threecomponents: (1) class-based revolts from below; (2) rapid and basic transformation of state struc-tures; and (3) rapid and basic transformation of class structures.3 Skocpol is explicit that if anyone of these three attributes is missing, the case in question cannot be considered a social revo-lution. In this sense, each of the three attributes isnecessaryfor social revolution. Skocpol alsostrongly implies that the simultaneous presence of the three components issufficientfor an eventto be classified as a social revolution: any case that contains her three components is definitely asocial revolution.
Given that Skocpol uses a necessary and sufficient approach to defining the outcome vari-able, it is appropriate to use AND in specifying the relationship between Skocpol’s three defi-nitional components and social revolution. When the two-level structure of outcome variable isadded to the two-level structure of the causal variables, the full argument depicted in figure 1emerges.
Burawoy’s (1989) critique of Skocpol shows how important, and how difficult, it is to see thecomplete causal structure of Skocpol’s argument. His table 1 (p. 768) clearly divides variables intotwo levels, and he correctly identifies peasant revolt and state crisis as the basic-level variables.However, he sees Skocpol as employing a necessary condition linkage between the basic andsecondary levels:
The task now is to show that both international pressure and an ‘organized and in-dependent dominant class with leverage in the state’ were necessary ingredients forpolitical crisis . . . So far so good, but note immediately that the contrasting cases[Germany and Japan] do not demonstrate ‘international pressure’ as necessary for thedevelopment of a revolutionary political crisis. In the next chapter Skocpol exam-ines the necessary conditions for the second component of revolution: peasant revolt. . . She now has to demonstrate that both political crisis and peasant autonomy werenecessary for peasant revolt. (p. 766)
Much of his argument against Skocpol collapses once it is clear that the relationship between levelsis one of equifinality and not necessary conditions.
We suggest that much of the debate around Skocpol can be traced to confusion about whatvariables belong to which levels and the structural relationships between levels. Not surprisingly,as we shall see below, this has important ramifications for theory testing.
Other Two-Level Theories
Skocpol is not alone in her use of a two-level theory; in fact, prominent analysts present theoriesthat have the same basic structure of Skocpol’s two-level theory (e.g., Linz and Stepan 1996).
3The first component is actually somewhat problematic, given that it may be causally related to the other two,thereby raising questions of endogeneity.
10
However, other analysts have formulated two-level theories that vary from Skocpol’s in at leasttwo ways. First, whereas Skocpol primarily explores a causal relationship between levels, otherscholars examine substitutability or ontological relationships. Second, whereas Skocpol’s theoryidentifies a set of necessary conditions that are jointly sufficient at the basic level, other scholarsexamine equifinality at the basic level (i.e., individually sufficient causes).
A Substitutable Relationship: Ostrom. An excellent example of a two-level theory that usesa substitutablerelationship between the secondary and basic level is the work of Ostrom (1991).Ostrom identifies eight conditions4 that are necessary for her key outcome of “institutional func-tioning.” Of these eight conditions, monitoring and sanctions stand out. In fact, in her APSA presi-dential address, she selects them for special attention: “Most robust and long-lasting common-poolregimes involve clear mechanisms for monitoring rule conformance and graduated sanctions forenforcing compliance” (Ostrom 1998, p. 8). Thus, her argument emphasizes necessary conditionsthat form a conjuncture that is sufficient. In figure 2, we have represented this basic-level theoryby focusing on how “monitoring” and “sanctions” are individually necessary and jointly sufficientfor the outcome of institutional functioning (see Goertz 2003 for an elaboration of this model).
At the secondary level, Ostrom identifies variables that are specific means of sanctioningand monitoring, thereby employing a substitutable relationship between levels. Ostrom identifiestwo ways that monitoring can be accomplished: monitoring by an institutional member or moni-toring by a paid agent. Clearly, these two types neither cause nor define the basic-level variable ofmonitoring. Analogously, the basic-level cause of sanctions can be arrived at in one of two ways:sanctions by institutional officials or sanctions by the paid police. Again, the relationship hereis one equifinality: institutional-official sanctions or paid-police sanctions are alternative paths tosanctions in general.
Here we see a typical example of how the basic level focuses on a factor common, e.g.,monitoring, to all successful common pool resource institutions. The secondary level is then ananalysis of how different societies with different resource technologies go about implementing amonitoring system. At the basic level the key fact is that there is monitoring; the secondary levelshows the substitutable ways in which this can occur in different cases. In other words, we havea situation of equifinality in which the secondary-level variables are individually sufficient for thebasic-level variable, as represented by the OR in figure 2.
Cioffi-Revilla (1998) and Cioffi-Revilla and Starr (2002) provide a mathematical and prob-abilistic analysis of a model with the same structure as Ostrom’s. Most and Starr introduced the in-fluential notion of foreign policy substitutability (Most and Starr 1984).5 They are also well-knownfor the idea that opportunity and willingness are individually necessary and jointly sufficient forforeign policy action. If one puts opportunity and willingness at the basic level and foreign policysubstitutability at the secondary level, one arrives at the model in figure 2. Cioffi-Revilla and Starr(2002) formally model this in ways that make clear the tight link with our analysis of two-levelmodels and they do so in a completely probabilistic fashion.
Beyond the Cioffi-Revilla and Starr example, we believe that two-level theories that pro-pose substitutable relationships are reasonably common, particularly in the comparative-historicalliterature. For example, Kiser et al. (1995) adopt this theoretical structure in discussing three sub-stitutable means through which control of the crown could be achieved in early modern Europe:(1) executive control, (2) legislative control, and (3) judicial control. These different types then
4These are: (1) monitoring, (2) graduated sanctions, (3) clear boundaries and memberships, (4) congruent rules, (5)conflict resolution mechanisms, (6) recognized rights to organize, (7) nested units, and (8) collective-choice arenas (seeOstrom 1991, p. 180).
5See also the special issue of theJournal of Conflict Resolution2002 39(1).
11
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enter into their overall causal argument about the occurrence of war itself. Likewise, Luebbert’s(1987) study of interwar regimes in Europe uses the same logic in making the following argu-ment about two types of corporatism: “Where liberal parties had failed to establish responsibleparliamentary institutions before the war, it would prove impossible to stabilize a pluralist democ-racy afterward. Henceforth, stabilization would require corporatism – in either its fascist or socialdemocratic variants” (p. 449). Hence, fascism and social democracy were substitutable means forachieving stability once the opportunity for liberal democracy was foregone.
An Ontological Relationship: Downing. Downing’s (1992)The Military Revolution and Po-litical Changeoffers a two-level theory of the origins of liberal democracy in early modern Eu-rope (see figure 3). At the basic level, Downing identifies two main causes that are individuallynecessary and jointly sufficient for liberal democracy: (1) medieval constitutionalism – i.e., aninstitutional heritage that included representative assemblies and other constitutional features; and(2) the absence of military revolution – i.e., little or no domestic mobilization of resources forwar-fighting purposes during the sixteenth and seventeenth centuries.6
In the two-level theory, the medieval constitutionalism variable is constituted by four secondary-level variables that literally are “medieval constitutionalism.” Thus, according to Downing, me-dieval constitutionalism is “parliaments controlling taxation and matters of war and peace; localcenters of power limiting the strength of the crown; the development of independent judiciariesand the rule of law; and certain basic freedoms and rights enjoyed by large numbers of the popula-tion” (p. 10). As figure 3 shows, Downing uses the classical necessary and sufficient approach toconcept membership when modeling medieval constitutionalism (as indicated by the AND in thefigure). These ontological secondary-level variables enter into the causal analysis because theyaffect the possibility of democracy. For example, if a country lacks one or more of the defin-ing attributes of medieval constitutionalism (e.g., independent judiciaries), then that country willalso lack an essential prerequisite (i.e., necessary condition) for democracy. Hence, ontologicalsecondary-level variables are causally related to the main outcome variable at the basic level.
For the basic-level cause of “absence of military revolution,” the relationship with the sec-ondary level is one of equifinality. Four secondary-level variables are alternative causes of theabsence of a military revolution. Thus, when faced with heavy warfare, a country can avoid asubstantial mobilization of national resources toward the military if one or more of the followingcauses are present: (a) a geography that provides a natural barrier to invading armies, (b) commer-cial wealth that allows the country to protect itself while mobilizing only a proportion of resourcestoward war, (c) foreign resource mobilization that takes place when war is conducted primarilyoutside a country’s territory, and (d) alliances that reduce the extent of domestic resources thatmust be mobilized (pp. 78–79, 240). A key aspect of Downing’s argument involves exploring thedifferent ways that specific countries avoided a military revolution and stayed on a path leading todemocracy.
Equifinality: Hicks et al. Ragin’s (1987; 2000) discussions of qualitative comparative analysis(QCA) and fuzzy-set analysis are centrally concerned with the following logical structure: equifi-nality at the basic level and necessary conditions at the secondary level. By contrast, the examplesdiscussed so far tend to have the converse structure: a conjuncture of necessary conditions at thebasic level and mostly equifinality at the secondary level. We do not believe that the logical modelon which we have focused is more important than the typical QCA/FS one, but rather that it needs
6In his words: “To put the argument in its barest form, medieval European states had numerous institutions, pro-cedures, and arrangements that, if combined with light amounts of domestic mobilization of human and economicresources for war, provided the basis for democracy in ensuing centuries” (1992, p. 9).
13
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to be recognized as powerful and common in its own right. In this section, however, we considerthe logical structure more familiar in QCA/FS analyses.
We examine the two-level theory developed in Hicks, Misra, and Nah Ng’s (1995) QCAanalysis (see figure 4). The outcome variable of this study is the creation of welfare states duringthe crucial period of social provision expansion in the 1920s. This outcome is conceptualized usingthe family resemblance approach to concepts. Thus, a country is coded as a “welfare state” if itadopts at least three of four classic welfare programs: (1) old age pensions; (2) health insurance;(3) workman’s compensation; and (4) unemployment compensation. Here we have an equafinalityrelationship between secondary-level variables and the outcome variable: no single condition isnecessary; there are multiple paths to the category of welfare state.
At the basic level, the structure of the causal theory is also one of equifinality. The mainsecondary-level variables are: working-class mobilization, patriarchal state, unitary democracy,catholic government, and liberal government. In figure 4, we list the abbreviations for these vari-ables. The QCA results yield a relatively parsimonious model that is consistent with previoustheory yet enriches it in other ways. In the final model, there are respectively “three routes tothe early consolidation of the welfare state . . . (1) a ‘Bismarckian’ route, (2) a unitary-democratic‘Lib-Lab’ [i.e., Liberal-Labor] route, and (3) a Catholic paternalistic unitary-democratic route”(p. 344). The routes are represented by the following variable summaries: (1) WORK * PATRI-ARCHY * catholic * unitary-democracy; (2) WORK * UNITARY-DEMOCRACY * catholic; and(3) WORK * PATRIARCHY * CATHOLIC * UNITARY-DEMOCRACY * liberal. In presentingthese equations, we follow the standard QCA practice of designating variables that are presentwith capital letters and those that are absent with lower-case letters.
This QCA analysis thus arrives at substantively important findings. Working-class mobiliza-tion is necessary but not sufficient condition for a causal path to a welfare state. In the Bismarckianpath, working-class mobilization combines with a patriarchal authoritarian regime to produce awelfare state. In the other two routes, welfare states emerge in democracies facing working-classmobilization, either under the support of Liberals or under the support of Catholics in a contextof patriarchy. Though scholars have discussed the important role of Liberals in creating welfarestates, Hicks and his collaborators suggest that the Catholic path to welfare consolidation was alsocritical.
Indicators versus Secondary-Level Variables
It is tempting to think of the relationship between levels as one between variables (basic level) andindicators (secondary level), where “measurement” theory links the two. However, this temptationshould be avoided since the theoretical and formal relationships between variables and indicatorsare radically different from those between the basic and secondary levels. It is instructive to useLISREL models to illustrate this contrast between a variable-indicator approach and a two-leveltheoretical relationship.
The most fundamental difference between the two approaches concerns causation. In a two-level theory, the secondary-level variables always play an important role in the causal explanationof the basic-level outcome variable. In contrast, in the LISREL (and latent variable approach ingeneral) way of thinking, indicators are not causes buteffectsof basic-level variables. Formally,the indicators are the outcome variables, whereas the latent (basic-level) variables are the causes.For example, with this “disease-symptom” model, test scores might be seen as effects of intelli-gence. Hence, the causal arrow goes in exactly the opposite direction as what we have describedfor two-level theories.
15
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This can be seen in the equations used to model the relationship between indicators andlatent variables:
Xi = γ1θ1 + γ2θ2 + εi (5)
The latent factorsθi thus almost instinctively are considered causes of the indicatorsXi. Glymourexpresses nicely how from the beginning latent variable analysis was given a causal interpreta-tion: “Consider factor analysis. Thurstone (1935) introduced factor analysis under an equivocalinterpretation, claiming that his factor analysis models were nothing but simplifications of data. . . Of course, Thurstone’s latent factors were immediately and almost universally interpreted ashypothetical causes” (1997, 203–4). In short, two-level models differ from LISREL ones in thedirection of the causal arrow between levels.
It also bears emphasis that the way in which indicators and secondary-level variables ag-gregate to the basic-level are different. Scholars who use indicators usually assume that the “av-erage” of various measures provides an indication of the degree to which a concept is present.But the average is fundamentally different than both the necessary/sufficient structure adopted inthe classical approach to concepts and the equifinality structure used with the family resemblanceapproach. For example, with the equifinality structure, the average score of different secondary-level variables is irrelevant; the only issue is whether a sufficient number of the secondary-levelvariables are present.
This point can be seen through a contrast with Bollen’s (1980) work on the concept ofdemocracy. His LISREL model theorizes democracy as a cause of multiple indicators. To de-velop a manageable measure of democracy, he recommends an average of three good indicators.For Bollen, the latent variable (i.e., the basic-level variable of democracy) is the cause of thesecondary-level variables. Democracy is the cause of political liberty and popular sovereigntyindicators, just as intelligence is often seen as the cause of performance on test items. In thiscontext, the best situation is when indicators are correlated, given that they are all products of thesame latent cause.
An ontological relationship between levels is especially likely to breed confusion with thevariable-indicator approach. Accordingly, in our discussion of the ontological relationship, wehave stressed the literature onconcepts, not the literature on indicators. It is fundamentally adifferent enterprise to analyze and discuss what democracyis than to discuss what should be theindicators of democracy. The literature on concepts, notably that by Collier and his colleagues,thinks and talks about concepts in terms of necessary conditions or equifinality as we do here.Thus, when thinking about ontology, one should turn to the literature on concepts instead of theliterature on indicators.
The Fuzzy-Set Methodology of Two-Level Theories
Given the complex relationships modeled in two-level theories, how can scholars test the propo-sitions of these theories? In this section, we argue that fuzzy-set analysis is an extremely usefulmethodology for carrying out this task. The advantages of fuzzy-set analysis for testing two-leveltheories include enabling researchers to logically analyze necessary and sufficient causation andallowing these researchers to code qualitative variables in light of their specialized knowledge ofparticular cases.
The application of fuzzy-set analysis can be complicated, even for relatively straightforwardcausal propositions. When we move to two-level theories, the issues are especially challenging.Thus, rather than offer superficial tests of multiple two-level theories, we choose instead to providea sustained consideration of one specific two-level theory: Skocpol’sStates and Social Revolutions
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(1979). We focus on Skocpol’s book because it is a well-known study that usefully highlightsmany of the challenges that arise in using fuzzy-set analysis to test two-level theories. Our goalis ultimately less to offer a definitive test of Skocpol’s argument and more to examine the generalmethodological issues that it raises.
Before beginning, it is worth underlining again that many critics of Skocpol have not ad-equately understood key elements of her two-level theory. In some cases, the problem has beenconfusion about levels. For example, in a widely-cited critique, Geddes (1990; also Geddes 2003)treats Skocpol’s secondary-level variables as if they directly affect the outcome of social revolutionitself. For example, she correlates international pressure (a secondary-level variable) directly withthe outcome of social revolution. Yet, as we have stressed, one cannot understand the effects ofSkocpol’s secondary-level variables on social revolution without understanding the equifinality re-lationship between levels. A weak correlation between international pressure and social revolutionis hardly evidence against Skocpol: international pressure does not matter for social revolution aslong as there is another secondary-level variable (i.e., dominant class leverage or agrarian back-wardness) to take its place.7 Likewise, even though Burawoy’s (1989) critique of Skocpol suggeststhat her model features two levels, he fails to clearly distinguish which secondary-level variablesgenerate which basic-level variables. Burawoy assesses Skocpol’s theory by exploring whetherthere is any relationship between state autonomy and peasant revolt, and between peasant auton-omy and state breakdown. Given her model, however, Skocpol would not expect any relationshipbetween these particular variables since they confuse the secondary-level variables that producestate breakdown with those that produce peasant revolt.
Beyond this, we also observe that many of Skocpol’s critics have not correctly representedthe causal structure of her theory at basic level itself. Most commonly, analysts proceed as ifSkocpol’s theory were modeling correlational causes in which variables are related to one anotherin a linear pattern. For example, Geddes (1990) frames her discussion of Skocpol in the context ofselection bias, as conventionally understood in statistical research. Yet, as Dion (1998) has pointedout, these issues of selection bias cannot be meaningfully extended to studies focused on necessarycauses. In short, from the previous methodological literature discussing Skocpol’s book, we caninitially underline two important lessons: (1) confusing basic-level and secondary-level variablesgrossly distorts any subsequent test of a two-level theory; and (2) confusing correlational relation-ships for relationships that are really modeling necessary or sufficient causes grossly distorts anysubsequent test of a two-level theory.
Coding the Variables
We begin our evaluation of Skocpol’s work by considering how fuzzy sets might be used to codeher outcome variable and causal variables at both the basic level and the secondary level.
Outcome Variable. Earlier we discussed Skocpol’s three-component definition of social revo-lution, noting that she treats each component as necessary and the combination of the three assufficient for membership in the category social revolution. Although Skocpol often sees variablesas either present or absent, her analysis makes it clear that many cases are neither fully “in” norfully “out” of a given dimension. On this basis, it is possible to use fuzzy sets to code cases acrossthe three secondary-level variables (see Table 2).8 To do this, we adopt a simple five-value coding
7In a subsequent analysis, Geddes (2003, pp. 114-116) treats international pressure as a necessary cause of socialrevolution. Again, however, our reading is that international pressure is one of several sufficient causes of the basic-levelvariable of state breakdown.
8We have gathered the key passages and evidence for these scores into an index that is available upon request.
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Table 2: Fuzzy-Set Test of Skocpol’s Theory: Outcome Variable
Secondary Level Basic Level
CountryClass State Class Social Social
Revolts Trans. Trans. Revolution RevolutionMinimum Min(SumXi,1)
France 1.00 1.00 1.00 1.00 1.00Russia 1917 1.00 1.00 1.00 1.00 1.00China 1.00 1.00 1.00 1.00 1.00England 0.00 1.00 0.25 0.00 0.42Russia 1905 1.00 0.00 0.00 0.00 0.33Germany 0.50 0.00 0.00 0.00 0.17Prussia 0.00 0.25 0.50 0.00 0.25Japan 0.00 1.00 0.25 0.00 0.42
scheme: 0.00, .25, .50, .75, 1.00. A more sophisticated approach to coding variables is not easilypursued given the inevitable qualitative distinctions developed inStates and Social Revolutions.
At least two strategies can be used for aggregating the fuzzy-set scores from the secondary-level into overall fuzzy-set scores of social revolution. One possibility is to use the classicalapproach based on AND as we did above – i.e., social revolution is a product of class-based revoltsandstate transformationsandclass transformations. In fuzzy-set analysis, AND is calculated bytaking theminimummembership score of each case in the sets that are intersected. Given that allthe cases besides France, Russia 1917, and China have a score of 0.00 for at least one secondary-level component, these cases also receive a score of 0.00 for social revolution. By contrast, sinceFrance, Russia 1917, and China have a score of 1.00 for all secondary-level variables, they alsoreceive a score of 1.00 for social revolution. This procedure of using the minimum leads to adichotomous coding of social revolution (see Table 2).
Second, an alternative aggregation procedure involves using the min(sumXi,1), which aswe noted above is appropriate for concepts built around the family resemblance structure. In thecase of Skocpol, we implement this procedure by dividing all values for secondary-level variablesby 3 and then summing the three variables together to generate a total score for social revolution.For example, the score for Japan is calculated as follows: 0/3 + 1/3 + .25/3 = .42. Clearly, as table2 shows, the use of the min(sumXi, 1) generates different values than the use of the minimum. Infact, no case has a score of 0.00 when the min(sumXi,1) is used, since at least one secondary-levelvariable is partially present for every case.
Using the min(sumXi,1) as an approach to creating scores for social revolution has twosupporting arguments. First, although Skocpol generally characterizes social revolution in a man-ner consistent with the minimum, her argument also suggests that she uses the sum of her threedefining attributes. In particular, Skocpol explicitly notes that she selected only “negative” casesthat were fairly close to becoming social revolutions, not cases that were maximally distant fromthe category social revolution. Thus, for example, her non-revolution cases do not include any in-stances of political stability and few situations where change did not occur at all. Instead, they allresemble social revolutions to some degree, and they all can be meaningfully seen as overlappingwith the category social revolution to at least some extent.
The second reason is that Skocpol’s dichotomous coding can also be derived from the aggre-gation procedure that uses the min(sumXi,1). Thus, table 2 shows that no case other than France,
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Table 3: Fuzzy-Set Test of Skocpol’s Theory: Secondary Level
State Breakdown Peasant Revolt
CountryInter. Class Agrarian Peasant Landlord
Pressure Leverage Backward Aut. Vulnerable
France 0.50 0.75 1.00 0.75 1.00Russia 1917 1.00 0.25 0.50 1.00 1.00China 0.75 0.75 1.00 0.00 0.75England 0.50 1.00 0.25 0.00 0.00Russia 1905 0.50 0.25 0.50 1.00 1.00Germany 0.25 0.25 0.25 0.50 0.00Prussia 0.75 0.25 0.25 0.50 0.00Japan 0.75 0.00 0.50 0.00 0.00
Russia 1917, and China receives a fuzzy-set score above .50. Hence, if these fuzzy-set scoreswere recoded dichotomously, one would still conclude that only these three countries experiencedsocial revolutions.
Secondary-Level Causal Variables. With regard to the causal variables, we begin with thesecondary level, because these variables are causally prior to those at the basic level. Skocpolmakes numerous observations about the degree to which each secondary-level cause is present.These observations provide a basis for coding the variables as fuzzy sets, a task which is carriedout in table 3.9
One of the interesting things to note about this table is that all of the cases have at least onecausal factor that is significantly present. Potentially, Skocpol selected her cases for precisely thisreason, believing that only countries in which one or more causal factors was largely present couldpossibly experience social revolution. Cases in which all causal factors are completely absent maynot have been included out of a conviction that social revolution was extremely unlikely in thesesettings (see Mahoney and Goertz 2004).
Basic-Level Causes. In a two-level theory, the values for basic-level causes are derived directlyfrom the values of the secondary-level causes. Hence, the methodological task of scoring basic-level causes is straightforward once the secondary-level variables are coded and the aggregationmethod is identified. In Skocpol’s theory, each secondary-level causal variable is individually suf-ficient for a particular basic-level cause. Thus, we can use OR to determine values for basic-levelcauses. In fuzzy-set analysis, the use of OR requires taking themaximumscore of the secondary-level variables. For example, France’s scores for the secondary-level variables that cause statebreakdown are 0.50, 1.00, and 0.75, and thus the case receives a score of 1.00 for state breakdown,since this is the highest score among the intersecting sets. We use this same procedure to arrive atall the scores for state breakdown and peasant revolt in table 4.
9The scores in this table reflect an ordinal coding of the cases that was independently carried out for a differentpurpose (see Mahoney 1999).
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Table 4: Fuzzy-Set Test of Skocpol’s Theory: Basic Level
CountryState Peasant State Breakdown* Social Social
Breakdown Revolt Peasant Revolt Revolution RevolutionMinimum Min(SumXi,1)
France 1.00 1.00 1.00 1.00 1.00Russia 1917 1.00 1.00 1.00 1.00 1.00China 1.00 0.75 0.75 1.00 1.00England 1.00 0.00 0.00 0.00 .42Russia 1905 0.50 1.00 0.50 0.00 .33Germany 0.25 0.50 0.25 0.00 .17Prussia 0.75 0.50 0.50 0.00 .25Japan 0.75 0.00 0.00 0.00 .42
Testing Two-Level Theory with Fuzzy-Set Analysis
This section provides the first ever reanalysis of Skocpol’s theory using fuzzy-set methods. Indeed,it offers the first ever fuzzy-set test of any two-level theory. Though we are focusing here onlyon Skocpol’s argument, in principle we believe that the many other two-level arguments withalternative causal structures could also be evaluated with fuzzy-set methods.
Testing Joint Sufficiency. We begin by testing Skocpol’s argument that state breakdown andpeasant revolt are jointly sufficient for social revolution. The column for “state breakdown*peasantrevolt” in table 4 gives the fuzzy-set values for this causal combination. The table also includescolumns with the two different scorings for the outcome variable depending on whether the mini-mum or the min(sumXi,1) is used. We first offer our best attempt to be faithful to the structure ofSkocpol’s argument, which entails using the minimum for the outcome.10 Likewise, since we can-not assume that Skocpol thinks of her variables in terms of continuous fuzzy-set scores, we beginby looking at results for dichotomous codes. This can easily be done in table 4 by converting allvalues of .50 or less to 0.00, and all values of greater than .50 to 1.00.
In dichotomous terms, Skocpol’s theory does quite well with respect to the proposition thatstate breakdown and peasant revolt are jointly sufficient for social revolution. It predicts accuratelyall the positive cases of social revolution: France, Russia 1917, and China. That is, all three ofthese cases have a dichotomous 1.00 in the column for “state breakdown*peasant revolt” and adichotomous 1.00 for social revolution. For the negative cases, the theory also correctly predictsa 0.00 (absence of social revolution) for England, Russia 1905, Germany, Prussia, and Japan.These results give us some confidence that our codes of the data are a reasonable approximationof Skocpol’s work and that we have correctly represented the structure of her theory.
When dichotomous codes are used, counting hits and misses is fairly straightforward. Oncewe move to fuzzy-set scores, however, it becomes more difficult to evaluate success and failure.The use of continuous fuzzy-set scores increases the probability that small coding errors will lead
10Strictly speaking, for the dichotomous test, either the minimum or the min(sumXi,1) could be used for the outcomevariable, since, as pointed out above, both procedures lead to a dichotomous coding in which only France, Russia 1917,and China are social revolutions.
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one or more cases to violate logical sufficiency or necessity. Since we have a complex modeland only approximate codings for the secondary-level variables, it is quite likely that our test willproduce one or more false negatives. Hence, we will consider a case to be consistent with causalsufficiency (or necessity) if its fuzzy-set value on the cause (or outcome) exceeds its score on theoutcome (or cause) by no more than one fuzzy membership unit, which in our coding schememeans a difference of no more than .25 (Ragin 2000; see also Goertz 2001). For example, weconsider the value for Germany of .25 for the joint combination of state breakdown and peasantrevolt to be close enough to the outcome value of 0.00 to be considered a success.
When the minimum is used to construct the outcome variable, the predictions of Skocpol’stheory (as reconstructed by us) suggest that we should see higher levels of social revolution intwo cases, Russia 1905 and Prussia (i.e., both cases have a fuzzy-set value of .50 for the causalcombination but a value of 0.00 for social revolution). With Russia, Skocpol argues that the Rev-olution of 1905 was nearly a full-blown social revolution, and only the abrupt end of internationalpressures allowed the country to temporarily avoid this fate (1979, p. 95). Given that this countrydid experience a social revolution about a decade later, the low value on the outcome for Russia1905 can perhaps be understood as an early measurement of a variable whose value was soon toincrease. As for Prussia, its low value on the outcome reflects the fact that class-based revoltswere not an important component of the reforms of 1807–14, leading the case to be coded as zerofor social revolution. Again, though, this low value was a temporary situation. By the time of theGerman reform movement in 1848, the value for the class revolts dimension of social revolutionwas .50. Hence, Prussia is not successful in the test because Junker landlords were able to keepclass-based revolts in check to a surprising degree, though they were not able to sustain this controland the country would soon more closely approximate a social revolution.
While not a miss by our standards, the China case merits discussion. The predicted valueis .75 or lower while the outcome is 1.00. A value less than 1.00 is predicted on the outcomebecause China receives only .75 on the basic-level cause of peasant revolt. Other analysts havepreviously raised concerns about Skocpol’s treatment of peasant revolt in China, suggesting thatit is not fully consistent with her theory (e.g., Taylor 1989; Selbin 1993). For her part, Skocpolargues that the Chinese Communist Party created a high level of peasant autonomy and solidarityonce the revolution was under way. If these organizational activities are taken into consideration,the Chinese case might be seen as having a 1.00 for the peasant revolt variable.
Looking at the min(sumXi,1) for social revolution provides an instructive contrast to Skocpol’suse of the minimum. The practical effect of using the min(sumXi,1) is to increase the value of thecases that have a zero with the minimum. Hence, the min(sumXi,1) makes it easier to find causalsufficiency, since the value of the outcome variable may be increased (but never decreased) com-pared to the minimum. For example, both Russia 1905 and Prussia are within the neighborhoodof causal sufficiency when the min(sumXi,1) is used for the outcome variable. Russia 1905 hasa value of .50 for the combination of state breakdown and peasant revolt, which is only slightlyabove its score of .33 for the outcome using the min(sumXi,1). Hence, if the min(sumXi,1) isused for the outcome variable, an even stronger case can be made that state breakdown and peas-ant revolt are jointly sufficient.
Testing Causal Necessity. The previous discussion offered a test of Skocpol’s theory about jointsufficiency for the basic-level variables. Here we explore the other central claim of her maintheory: state breakdown and peasant revolt are individually necessary for social revolution.
For the state breakdown variable, the data support the argument about causal necessity. Alleight cases have scores on the state breakdown variable that are greater than or equal to their scoreson the outcome within one fuzzy-set unit (i.e., within .25). We find this for both versions of the
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social revolution variable. This support for causal necessity is not unrelated to the way in whichthe basic-level causes were constructed from the secondary level. In particular, the maximum wasthe mode of creating the basic level, which gives the highest possible value for the basic-levelvariables. This mode of moving across levels makes it easier to support claims of causal necessity,since it produces a high value on the basic-level causes.
The necessity of peasant revolts depends heavily on how the outcome variable is coded.When the minimum is used, necessity is achieved for the non–social revolution cases because theyall have a value of zero on the outcome. Hence it is easy to have a larger or equal value on thepeasant revolt causal variable!
Once we move to the min(sumXi,1) for the outcome variable, however, Japan and Englandare no longer consistent with the argument about causal necessity. This lack of empirical support isdriven by the complete absence of peasant revolts combined with a reasonably high fuzzy-set scorefor social revolution (i.e., .42). We would suggest that Skocpol’s selection procedure might haveled her to this kind of contradictory case. Skocpol may have selected England and Japan preciselybecause peasant revolts were totally absent even though the cases resembled social revolutions incertain important respects. This kind of selection procedure in which a case is chosen because ithas a very low value on a causal variable but a reasonably high value on the outcome variable isalmost certain to violate causal necessity. Again, though, we emphasize that Skocpol most likelyprefers to think about the outcome variable in terms of the minimum, not the min(sumXi,1), andher cases are consistent when that approach is used.
In short, our analysis provides substantial support for Skocpol’s theory, though it also raisessome lingering questions about specific cases. Above all, the example shows how challenging itis to confirm a two-level theory that proposes, at the basic level, a set of variables that are individ-ually necessary and jointly sufficient. This is true because an aggregation procedure for movingfrom secondary-level variables to basic-level causes that makes it more likely to find necessityfor individual variables simultaneously makes it more difficult to find sufficiency for a combina-tion of these variables. For example, the maximum will produce high values for the basic-levelcauses, which in turn will make it easier to find causal necessity when these variables are testedwith fuzzy-set methods. At the same time, however, the use of the maximum for constructingbasic-level causes will make it more challenging to support claims that these variables are jointlysufficient, since this mode will inflate the value of the causal combination. Concerning the out-come variable, the minimum makes it easier to find causal necessity and more difficult to findcausal sufficiency when compared to the min(sumXi,1).
Two-Level Theories and the interpretation of QCA/FS
The Skocpol example illustrates how important the mode of aggregating secondary-level variablesto the basic level can be for testing theoretical claims. The results of the fuzzy-set test dependedin part on her use if the maximum for creating the basic-level causes. In this section, we brieflydiscuss alternative options for aggregating to the basic level. In addition, we assess the benefits ofreinterpreting QCA/FS results presented at a single level in terms of two levels.
QCA and fuzzy-set analyses generate single-level models where there are multiple paths tothe dependent variable. However, conceptualizing these models in terms of two levels can makethe interpretation of the results more coherent both formally and theoretically.
A not uncommon situation is when the final results of the QCA/FS analysis look like:
Y = (A ∗ B ∗ C) + (A ∗ B ∗ D) (6)
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Often it makes much theoretical and empirical sense to think of C and D as substitutes for eachother. Accordingly, one arrives at a two-level model such as:
Y = A ∗ B ∗ E (7)
E = C + D (8)
To reconceptualize QCA results in this fashion, the analyst must identify the concept E forwhich C and D can substitute. Typically, this will involve moving up the ladder of abstractionto a more general concept. For example, Amenta and Poulsen (1996) show that there are twonecessary conditions for new deal policies such as OAA pensions, voting rights, and absence ofpatronage politics. To achieve sufficiency, some mechanism for positively pushing reform throughgovernment must be present. This can happen in substitutable ways, e.g., ”administrative powers”or ”democratic or third parties” (see also Amenta et al. 1992). These substitutable means arelike variables C and D above, while the general idea of a mechanism for achieving reform is likevariable E above.
Snow and Cress (2000) in their analysis of the success of homeless social movements findthe same sort of pattern:
Six SMOs [social movement organizations] obtained positions on boards and taskforces that addressed the homeless issue [dependent variable]. Two pathways led tothis outcome. Organizational viability, diagnostic frames, and prognostic frames werenecessary conditions for obtaining representation. These conditions were sufficient incombination with either disruptive tactics, where allies were present, or nondisruptivetactics, in the context of responsive city bureaucracies (p. 1082).
Here too one sees the substitutability of power in the analysis. One needs either “allies” who areinfluential in the communityor a friendly city government to begin with. You do not use disruptivetactics with friends, while you do if the city government is unfriendly.
The key point is that often we can reinterpret QCA or fuzzy-set analyses in terms of two-level theories, particularly using the substitutability relationship. This is another reason why two-level theories provide a rich set of methodological tools: they can help make sense of the resultsof single-level models by reinterpreting them as two-level models.
Conclusion
Given the complexity of two-level theories, scholars would do well to explicitly state the theoret-ical structure of these arguments. Toward this end, we conclude with a series of questions thatmay be useful to scholars – both for approaching their own research and for analyzing the work ofothers.
First, is the main theory composed of necessary conditions that are jointly sufficient or doesit involve equifinality and multiple paths? In answering this question, it is crucial that the issue ofnecessity be considered separately from the issue of joint sufficiency. We have found that oftenscholars are reasonably clear that their causal variables are individually necessary, but they aremuch less clear whether the combination of these variables is sufficient.
Second, the same question needs to be asked about the relationship between the secondary-level variables and the basic-level variables. Because most theories propose multiple causes at thebasic level, the analyst must be address the specific secondary-level relationship for each of thesevariables. For one basic-level cause, the secondary-level relationship may be characterized byequifinality, whereas for another it may be characterized by a conjuncture of necessary conditions.
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Third, what is the structural relationship between levels – causal, ontological, or substi-tutable? Here scholars simply need to be explicit about the purpose of secondary-level variables:either they are intended to represent causes of the basic-level causes (causal relationship), or theyare features that constitute the basic-level causes (ontological relationship), or they are substi-tutable means to the basic-level causes (substitutable relationship).
Fourth, if the relationship involves equifinality, particularly at the secondary level, is themaximum or the min(sumXi,1) more appropriate? The choice will strongly influence basic-levelcoding and thus should be taken seriously. The best answer depends in part on whether a singlesecondary-level variable is sufficient for the basic-level causal variable or whether two or moresecondary-level variables from a larger pool must be present for the basic-level cause. As a generalrule, we suggest the maximum when a single variable is sufficient, and the min(sumXi,1) whentwo or more variables must be present for sufficiency. In addition, in all cases, the maximum hasadvantages over the min(sumXi,1) when secondary-level variables are highly correlated with oneanother.
In this article, we have given some examples of prominent works that implicitly use two-level models. While we do not pretend to know all works that use two-level models, the structureof this framework does appear prominently in several other analyses, including Blake and Adolino(2001), Ertman (1997), Goertz (2003), Jacoby (2001), Kingdon (1984), Linz and Stepan (1996),and Wickham-Crowley (1996). In particular, we have found the literature on states, public policy,and social movements/revolution to be rich in applications of two-level ideas. One of the goals ofthis article was to make explicit explanatory theories that a number of researchers have intuitivelyfound useful. Instead of reinventing two-level models each time, then, we hope an awareness oftheir properties will increase the methodological rigor of future work.
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